Such audio systems are for instance used in mobile phones for which devices the considered audio frequency is typically 10 Hz to 20 kHz. In such mobile applications size of components always matters. This holds true for electro-acoustic transducers like microphones and loudspeakers. The latter are disadvantaged as loudness directly deals with the amount of moved air within the loudspeaker. Higher sound level demands together with smaller size demands can only be realized, if all parts of the loudspeaker are optimally designed.
In order to fulfill the high sound level requirement, moved air volume needs to be maximized and floor space of the whole loudspeaker needs to be minimized. This leads to high excursions of the diaphragm which leads to a decreasing adaptability for a linear loudspeaker model.
A common way of modeling a loudspeaker basically in a linear matter consists of three parts as shown in FIG. 1:                The electrical model (consisting of a resistor Rconductor and the voice coil inductance Zcoil)        The mechanical model (consisting of the mass MMS, spring CMS and damping component RMS−1 of the moving diaphragm and voice coil)        The acoustic model (consisting of the acoustical mass Ma, the acoustical compliance Ca and the acoustical resistance Ra)        
This model can be used to predict the behavior of a loudspeaker if parameters are known. To gain most acoustic power out of the loudspeaker, all parts need to be adapted to the thermal and mechanical stress. The voice coil temperature due to the driving current needs to be taken into account as well as the excursion, which is limited by diaphragm design or even hard limited by basket or the magnet system. Taking the electrical, the mechanical and the acoustic model into account a main loudspeaker resonance frequency may be evaluated.
Spread in mechanical dimensions, production processes etc. lower the theoretical power limit of a loudspeaker. To augment this limitation two basic concepts have been developed in the past:
Motion Control of the Diaphragm by Additional Sensing Voice Coil
As described in the U.S. Pat. No. 4,327,250, a sensing voice coil is mounted in addition to the voice coil on the moving diaphragm and provides information about the diaphragm velocity. This information is used in the driver circuit to adjust the audio signal and limit the excursion of the diaphragm. To track not only the velocity, but also the absolute position of the diaphragm, a condenser principle can be used to obtain the relative position of the diaphragm.
Motion Control by Modeling the Motion
This approach is far more complicated, for it adapts a linear or even non-linear model to online measurements of the voice coil current and voltage. This model is based on static parameters like the magnetic flux B times the length of the voice coil wire, the known mass and the static resistance of the voice coil. Based on these model parameters and the measured values for current and voltage an excursion estimate can be computed and therefore controlled.
Drawbacks for these Two Basic Concepts
The true motion control as described in the U.S. Pat. No. 4,327,250 requires an additional sensing mechanisms (like the sensing voice coil and one or two additional sensor transducer connections) and wiring of this mechanism in addition to the transducer connections, but is robust against any spread in the whole transducer chain including the acoustic situation to which the loudspeaker is applied.
The modeling approach avoids additional transducer connections of the loudspeaker, but needs a lot of digital signal processing power and the results are only as robust as the model reflects the “real world”.